Answer
$x = 9.8$ inches
Work Step by Step
In similar triangles, corresponding sides are proportional to one another.
Let us set up a proportion to find the relationship between two sides of one triangle and two sides of the other triangle:
$\frac{7}{x + 7} = \frac{5}{12}$
Cross multiply to get rid of fractions:
$5(x + 7) = 7(12)$
Multiply to simplify:
$5x + 35 = 84$
Subtract $35$ from each side of the equation to move constants to one side of the equation:
$5x = 49$
Divide each side by $5$ to solve for $x$:
$x = 9.8$ inches
